Simplify the following expression: $r = \dfrac{3t^2 - 45t + 150}{t - 5} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $3$ , so we can rewrite the expression: $ r =\dfrac{3(t^2 - 15t + 50)}{t - 5} $ Then we factor the remaining polynomial: $t^2 {-15}t + {50} $ ${-5} {-10} = {-15}$ ${-5} \times {-10} = {50}$ $ (t {-5}) (t {-10}) $ This gives us a factored expression: $\dfrac{3(t {-5}) (t {-10})}{t - 5}$ We can divide the numerator and denominator by $(t + 5)$ on condition that $t \neq 5$ Therefore $r = 3(t - 10); t \neq 5$